1997 ELorado Radiator Fan Speed

My engine temperature keeps going up and down. I mean from normal to hot. When the fan final go faster it will cool down the engine down. I have seen the fan run at different speeds. My question is does the fan have more than 1 speed. If so could the thermostat that controls the speed be bad. If so could it be the plug at the top of the radiator with 2 wires coming out of it. Thanks for your help.